Determine the expected value, variance, and standard deviation of 1/ 2*square root x?

X f(x) dx .......=?(x = 1 to 4) x ((1/4) x^(-1/2)) dx .......=?(x = 1 to 4) (1/4) x^(1/2) dx .......= (1/4)(2/3) x^(3/2) {for x = 1 to 4} .......= 7/6. ---------------- E(X^2) =? X^2 f(x) dx .......=?(x = 1 to 4) x^2 ((1/4) x^(-1/2)) dx .......=?(x = 1 to 4) (1/4) x^(3/2) dx .......= (1/4)(2/5) x^(5/2) {for x = 1 to 4} .......= 31/10.

Var X = E(X^2) - (E(X))^2 .........= 31/10 - 49/36 = 313/180. Std. Dev = sqrt(313/180).

I hope this helps!

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